Anisotropies in the Diffuse Gamma-ray Background Measured by the Fermi-LAT Eiichiro Komatsu (Texas Cosmology Center, UT Austin) in collaboration with J. Siegal-Gaskins, A. Cuoco, T. Linden, M.N.Mazziotta, and V. Vitale (on behalf of Fermi-LAT Team) DEUS, Dark Cosmology Centre August 8, 2011
Motivation • How can we see photons from annihilation/decay of dark matter particles? 2
Conventional Method • Use the energy spectrum of the mean intensity (the number of photons averaged over the sky), and look for spectral features. However , dark matter is not the only source of gamma-ray photons. How can we distinguish between dark matter signatures and astrophysical sources? 3
Diemand, Khlen & Madau, ApJ, 657, 262 (2007) Annihilation Signals from Milky Way •Why focus only on the energy spectrum? •Perhaps we can use the spatial distribution. 5
And, not just Milky Way! Dark matter particles are annihilating (or decaying) everywhere in the Universe! •Why just focus on Milky Way? While we cannot resolve individual dark matter halos, the collective signals can be detected in the diffuse gamma-ray background. How can we detect such signatures unambiguously? 7
Ando & EK (2006); Ando, EK, Narumoto & Totani (2007) Gamma-ray Anisotropy Dark matter halos trace the large-scale structure Therefore, the gamma-ray background must be anisotropic. If dark matter particles annihilate or decay, anisotropy must be there. And, their spatial distribution can be calculated within the framework of Lambda-CDM model (using analytical calculations or numerical simulations) 8
Using Fermi Data, just like WMAP WMAP 94GHz Fermi-LAT 1–2 GeV 9
Deciphering Gamma-ray Sky Astrophysical : Galactic vs Extra-galactic Galactic origin (diffuse) •E.g., Decay of neutral pions produced by cosmic-rays interacting with the interstellar medium. Extra-galactic origin (discrete sources) •Active Galactic Nuclei (AGNs) •Blazars (Blazing quasars) •Gamma-ray bursts Exotic : Galactic vs Extra-galactic Galactic Origin •Dark matter annihilation in the Galactic Center •Dark matter annihilation in the sub-halos within the Galaxy Extra-galactic Origin •Dark matter annihilation in the other galaxies 10
Blazars Blazars = A population of AGNs whose relativistic jets are directed towards us. Inverse Compton scattering of relativistic particles in jets off photons -> gamma-rays, detected up to TeV How many are there? (They are rare.) EGRET found ~70 blazars (out of ~100 associated sources) over the full sky Fermi-LAT found ~570 blazars (out of ~820 associated sources) over the full sky (LAT 1FGL catalog) 11
Diffuse Gamma-ray Background • First, we remove all the resolved (detected) sources from the Fermi-LAT map. • Then, calculate the mean intensity of the map as a function of energies. • The intensity includes contributions from unresolved sources (below the detection threshold) and truly diffuse component (if any). 12
Fermi-LAT Collaboration, ApJ, 720, 435 (2010) Unresolved blazars are not enough to explain the background all blazars • What constitutes BL Lac Flat-spectrum the rest? radio quasars 13
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Data Analysis • Use the same Fermi-LAT map (~22mo, diffuse-class events) • Apply the usual spherical harmonics transform, and measure the power spectrum! • I (n) = ∑ lm a lm Y lm (n) • C l = (2l+1) –1 ∑ m | a lm | 2 • Just like we did for the analysis of the CMB maps measured by WMAP . 15
1.0–2.0 GeV Mask |b|<30 degrees 16
2.0–5.0 GeV Mask |b|<30 degrees 17
5.0–10.4 GeV Mask |b|<30 degrees 18
10.4–50.0 GeV Mask |b|<30 degrees 19
Fermi vs WMAP • There is an important difference between Fermi and WMAP maps • We count photons to produce Fermi maps; thus, there is the “photon noise” (Poisson statistics) in the power spectrum, which we must subtract. • Photon noise, C N , is independent of multipoles, and is given by the mean number density of photons over the sky (which is precisely calculable). 20
Point Spread Function • The measured power spectrum is the true power spectrum multiplied by the harmonic transform of the “point spread function” (PSF). (It is called the “beam transfer function” in the WMAP analysis.) • PSF is by no means a Gaussian - we use two different versions of Fermi-LAT instrument response functions and compute PSF. • We then compute • The attenuation by PSF is corrected as (C l –C N )/W l2 . • Two versions of PSF gave consistent answers. 21
Photon noise has been subtracted 1.0–2.0 GeV 22
Photon noise has been subtracted 2.0–5.0 GeV 23
Photon noise has been subtracted 5.0–10.4 GeV 24
Photon noise has been subtracted 10.4–50.0 GeV 25
Observations • At l<150, the power spectrum rises towards lower multipoles (larger angular scales). • The Galactic foreground contribution (more later) • At l>150, we detect the excess power over the photon noise. • The excess power appears to be constant over multipoles, indicating the contribution from unclustered point sources (more later) 26
DATA: CLEANED = Galactic Model Map Subtracted 1.0–2.0 GeV 27
DATA: CLEANED = Galactic Model Map Subtracted 2.0–5.0 GeV 28
DATA: CLEANED = Galactic Model Map Subtracted 5.0–10.4 GeV 29
DATA: CLEANED = Galactic Model Map Subtracted 10.4–50.0 GeV 30
Focus on l>150 • The Galactic model maps indicate that the power we see at l<150 is largely coming from the Galactic foreground. • The small-scale power at l>150 is not very much affected by the foreground, and thus is usable for investigating the extra-galactic gamma-ray background . 31
No Scale Dependence • Fitting the measured power spectrum at l>150 to a single power-law: C l ~ l n Therefore, we will find the best-fitting constant power, C P . (“P” stands for “Poisson contribution”) 32
First detection of the extra- galactic γ -ray anisotropy • Many-sigma detections up to 10 GeV! 33
Energy Spectrum Consistent with a single power-law. For C P ~E –2 Γ , (statistical errors only) Raw Data: Γ =2.40 ±0.07 Cleaned Data: Γ =2.33 ±0.08 34
Fermi-LAT Collaboration, ApJ, 720, 435 (2010) Are we seeing blazars? Distribution of energy spectrum indices of detected blazars • The energy spectrum of anisotropy (from unresolved sources) agrees with that of detected blazars. 35
Interpreting the Results • Unresolved, unclustered point sources contribute to C P as • Unresolved, point sources contribute to the mean intensity as < I > • Are they consistent with the data?
The answer seems YES • Our results are consistent with the following interpretation: • The detected anisotropy is largely due to unresolved blazars. • The amplitude of anisotropy is consistent with the fact that the same unresolved blazars contribute only to a fraction of the mean gamma-ray background. • These two, independent measurements give us a consistent picture of the gamma-ray sky. 37
Another Look • Define the “dimensionless fluctuation power” by dividing C P by the measured mean intensity squared: • C P -> C P /<I> 2 ~ 0. 91 ( 0.69 )± 0.08 x 10 –5 sr (statistical errors only) 38
What about Dark Matter? • Our results can be used to place limits on the dark matter properties. • Subtracting the blazar contribution, the upper limit on the constant power at l>150 is • C P /<I> 2 < 10 –6 sr • What would this mean? 39
Ando & EK (2006); Ando, EK, Narumoto & Totani (2007) 2006/2007 Predictions DM ann. Blazars /<I> 2 • Watch out for the factor of l(l+1). • Poisson spectrum Dark matter gives ~l 2 predictions are • We constrain C l only still consistent with data, but at l>150 not so far away! 40
Bottom-line Message • We have the new observable: power spectrum of the gamma-ray background . • And, it has been detected from the data. 41
Conclusions • We have detected anisotropy in the extra-galactic diffuse gamma-ray background from Fermi-LAT 22mo maps. • The detected anisotropy is consistent with the contribution from unresolved blazars • Also consistent with the mean intensity data • The origin of the bulk of diffuse background remains a mystery • Dark matter annihilation contributions may not be so far away from the current limit. Wait for results from the future Fermi analysis (3 to 7 more years to go!) 42
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